The response of a wireless communication channel is estimated by a wireless receiver so that the receiver can coherently demodulate received data symbols. Channel estimation is typically performed using known symbols referred to as pilot symbols. Pilot symbols are transmitted in the time-frequency domain in OFDM (Orthogonal Frequency-Division Multiplexing) systems. The pilot symbols sample the time-frequency response of the OFDM channel which is a slow-varying, two-dimensional process. The response of an OFDM channel is conventionally estimated based on pilot symbols using minimum mean-square error estimation (MMSE), maximum-likelihood (ML) estimation or other approaches that are suboptimal such as interpolation.
MMSE channel estimation typically requires prior knowledge of channel statistics and tends to be highly complex because of the matrix inversion performed during the channel estimation process. The size of the matrix inversion performed by an MMSE estimator depends on the number of pilot symbol observations. In OFDM systems, pilot symbol density must be sufficiently large so that receiving devices can properly reconstruct an accurate representation of the time-frequency channel response. This in turn can dramatically increase the size of the matrix inversion performed by an MMSE channel estimator, significantly increasing MMSE estimation complexity. ML channel estimation also tends to be relatively complex, but not as complex as MMSE estimation. When pilot symbols are regularly spaced, ML estimation can be implemented using a two-dimensional FFT (fast-Fourier transform) process that yields the channel response in the delay-Doppler domain.
The complexity of both MMSE and ML estimators tends to increase significantly when pilot symbol spacing is irregular. Many types of OFDM systems have high pilot symbol density and irregular pilot symbol spacing. For example, the downlink specified in IEEE (the Institute of Electrical and Electronics Engineers) standard 802 16e (WiMAX) has 120 pilots for each OFDM symbol. Pilot spacing is also irregular, meaning that pilot symbols are transmitted at different time and frequency intervals. The Long Term Evolution (LTE) standard specified in Release 8 of 3GPP (3rd Generation Partnership Project) also calls for irregular pilot symbol spacing. The matrix inversion performed by a conventional MMSE estimator increases significantly when pilot symbol spacing is irregular. The complexity of a conventional ML estimator also increases when the estimator processes irregularly-spaced pilot symbols. An interpolation-based technique can be used to perform channel estimation when pilot symbol density is relatively high, but is sub-optimal and sacrifices accuracy for less complexity.